from wikipedia: http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser (4/20/2015)
From the Wikipedia article
The experimental setup, described in detail in Kim et al.,1 is illustrated in Fig 2. An argon laser generates individual 351.1 nm photons that pass through a double slit apparatus (vertical black line in the upper left-hand corner of the diagram). An individual photon goes through one (or both) of the two slits. In the illustration, the photon paths are color-coded as red or light blue lines to indicate which slit the photon came through (red indicates slit A, light blue indicates slit B). So far, the experiment is like a conventional two-slit experiment. However, after the slits, spontaneous parametric down conversion (SPDC) is used to prepare an entangled two-photon state. This is done by a nonlinear optical crystal BBO (beta barium borate) that converts the photon (from either slit) into two identical, orthogonally polarized entangled photons with 1/2 the frequency of the original photon. The paths followed by these orthogonally polarized photons are caused to diverge by the Glan-Thompson Prism. One of these 702.2 nm photons, referred to as the "signal" photon (look at the red and light-blue lines going upwards from the Glan-Thompson prism) continues to the target detector called D0. During an experiment, detector D0 is scanned along its x-axis, its motions controlled by a step motor. A plot of "signal" photon counts detected by D0 versus x can be examined to discover whether the cumulative signal forms an interference pattern. The other entangled photon, referred to as the "idler" photon (look at the red and light-blue lines going downwards from the Glan-Thompson prism), is deflected by prism PS that sends it along divergent paths depending on whether it came from slit A or slit B. Somewhat beyond the path split, the idler photons encounter beam splitters BSa, BSb, and BSc that each have a 50% chance of allowing the idler photon to pass through and a 50% chance of causing it to be reflected. Ma and Mb are mirrors.
Figure 3. x axis: position of D0. y axis: joint detection rates between D0 and D1, D2, D3, D4 (R01, R02, R03, R04). R04 is not provided in the Kim article, and is supplied according to their verbal description.
Figure 4. Simulated recordings of photons jointly detected between D0 and D1, D2, D3, D4 (R01, R02, R03, R04) The beam splitters and mirrors direct the idler photons towards detectors labelled D1, D2, D3 and D4. Note that: If an idler photon is recorded at detector D3, it can only have come from slit B. If an idler photon is recorded at detector D4, it can only have come from slit A. If an idler photon is detected at detector D1 or D2, it might have come from slit A or slit B. The optical path length measured from slit to D1, D2, D3, and D4 is 2.5 m longer than the optical path length from slit to D0. This means that any information that one can learn from an idler photon must be approximately 8 ns later than what one can learn from its entangled signal photon. Detection of the idler photon by D3 or D4 provides delayed "which-path information" indicating whether the signal photon with which it is entangled had gone through slit A or B. On the other hand, detection of the idler photon by D1 or D2 provides a delayed indication that such information is not available for its entangled signal photon. Insofar as which-path information had earlier potentially been available from the idler photon, it is said that the information has been subjected to a "delayed erasure". By using a coincidence counter, the experimenters were able to isolate the entangled signal from photo-noise, recording only events where both signal and idler photons were detected (after compensating for the 8 ns delay). Refer to Figs 3 and 4. When the experimenters looked at the signal photons whose entangled idlers were detected at D1 or D2, they detected interference patterns. However, when they looked at the signal photons whose entangled idlers were detected at D3 or D4, they detected simple diffraction patterns with no interference. Significance This result is similar to that of the double-slit experiment since interference is observed when it is not known which slit the photon went through, while no interference is observed when the path is known.
Figure 5. Raw results at D0 (with ambient illumination removed) will not reveal interference, which has important implications in regards to the possibility of using delayed choice quantum eraser results to violate causality. However, what makes this experiment possibly astonishing is that, unlike in the classic double-slit experiment, the choice of whether to preserve or erase the which-path information of the idler was not made until 8 ns after the position of the signal photon had already been measured by D0. Detection of signal photons at D0 does not directly yield any which-path information. Detection of idler photons at D3 or D4, which provide which-path information, means that no interference pattern can be observed in the jointly detected subset of signal photons at D0. Likewise, detection of idler photons at D1 or D2, which do not provide which-path information, means that interference patterns can be observed in the jointly detected subset of signal photons at D0. In other words, even though an idler photon is not observed until long after its entangled signal photon arrives at D0 due to the shorter optical path for the latter, interference at D0 is determined by whether a signal photon's entangled idler photon is detected at a detector that preserves its which-path information (D3 or D4), or at a detector that erases its which-path information (D1 or D2). Some have interpreted this result to mean that the delayed choice to observe or not observe the path of the idler photon changes the outcome of an event in the past. However, the consensus contemporary position is that retrocausality is not necessary to explain the phenomenon of delayed choice. Note in particular that an interference pattern may only be pulled out for observation after the idlers have been detected (i.e., at D1 or D2). The total pattern of all signal photons at D0, whose entangled idlers went to multiple different detectors, will never show interference regardless of what happens to the idler photons. One can get an idea of how this works by looking at the graphs of R01, R02, R03, and R04, and observing that the peaks of R01 line up with the troughs of R02 (i.e. a π phase shift exists between the two interference fringes). R03 shows a single maximum, and R04, which is experimentally identical to R03 will show equivalent results. The entangled photons, as filtered with the help of the coincidence counter, are simulated in Fig. 5 to give a visual impression of the evidence available from the experiment. In D0, the sum of all the correlated counts will not show interference. If all the photons that arrive at D0 were to be plotted on one graph, one would see only a bright central band.
I am puzzled about a few things related to the above:
a) What would happen if we did NOT detect an interference at $D_0$ 8ns prior to the entangled idler photons reaching $D_3$ or $D_4$ and decide to remove the $BS_a$ and $BS_b$ beam splitters really really fast such that the idler photons would travel to either $D_1$ or $D_2$ instead, hence the "which path" is not known and therefore we should actually see an interference pattern at $D_0$.
But we already got the "no interference" result 8ns prior, so something should stop us from doing this. Would the universe cause us to have a heart attack to keep us from messing with it?
(Possibly we could arrange the experiment in a way which would give us more than 8ns to remove $BS_b$ and $BS_a$ if the time-interval is too short, through the use Fiber optics cables, etc)
b) If we moved either the mirror $M_b$ or $M_a$ just a tiny little bit from its position, such that the red or blue path for the photon would be a bit different in length, wouldn't then we be able to tell via the time it took to reach either $D_2$ or $D_1$ detectors which of the two slits it came from?
Does this experiment really rely that much on getting mirror $M_a$ and $M_b$ at EXACTLY the right positions, for the paths to be EXACTLY the same, such that if the blue/red path differ only by 1 nano-meter the universe would "register" that and would "know" the "which path" can be extracted from that?
c) If we replaced $D_0$ with another double split, with the red and blue path each pointed at one of the two slits. Would in the case of the idler photon reaching $D_3$/$D_4$, the signal photon choose exactly one of the slits, hence not interfere with itself?
Therefore, in case of the signal photon hitting an area of the screen it could not possibly hit when interfering with itself (gaps on an interference pattern), we would know for certain that the which path is known 8ns beforehand with just a single photon pair (signal/idler), in this special case?
Again, we could possibly extend those 8ns to about 1 second for example, if we placed two 300000km long coiled fibre optics cables between PS and $BS_a$/$BS_b$.